A248836 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 2 times.

1, 2, 6, 22, 96, 482, 2736, 17302, 120576, 917762, 7574016, 67354582, 642041856, 6530291042, 70589700096, 808090395862, 9766250151936, 124258689304322, 1660195646078976, 23239748527125142, 340125128186658816, 5194627679316741602, 82645634692238278656

Offset: 0

Author

R. H. Hardin, Oct 15 2014

Keywords

• nonn

Comments

Column 2 of A248842

Examples

			Some solutions for n=6
..1....1....1....1....1....0....1....0....0....0....1....0....1....1....1....0
..0....2....2....0....2....2....2....2....2....1....1....1....2....0....0....1
..0....3....0....1....2....1....2....1....1....1....0....3....0....1....2....0
..1....4....0....0....4....2....0....3....3....2....3....3....4....0....0....2
..4....0....3....4....3....4....4....0....1....5....4....2....2....2....2....4
..5....6....4....5....4....0....3....6....6....5....0....2....5....4....4....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 0..210

Crossrefs

Cf. A000111, A248842.

Formula

From Seiichi Manyama, Feb 17 2025: (Start)

Conjecture: E.g.f.: 1/(1 - sin(x))^2.

If the above conjecture is correct, the following general term is obtained:

a(n) = Sum_{k=0..n} (k+1)! * i^(n-k) * A136630(n,k), where i is the imaginary unit. (End)

Conjecture from Mikhail Kurkov, Jun 26 2025: (Start)

a(n) = R(n+1,0) where

R(0,0) = 1,

R(n,k) = Sum_{j=0..n-k-1} R(n-1,j) for 0 <= k < n,

R(n,n) = Sum_{j=0..n-1} R(n,j). (End)

Extensions

a(0)=1 prepended by Seiichi Manyama, Feb 17 2025